Russia is ready for talks with the United States about a withdrawal of all Syrian rebels from eastern Aleppo as Syrian government forces advance deeper into the former rebel stronghold.

Moscow has proposed setting up four humanitarian corridors into east Aleppo as Syrian government forces - backed by Russia - now control more than half of the eastern part of the city.

"We have informed the UN in New York and Geneva that there is no longer a problem with the delivery of humanitarian cargo to eastern Aleppo," Russia's Foreign Minister Sergei Lavrov said Friday.

He said the UN was coming up with a plan and approval from Syrian authorities remained essential.

Tens of thousands of civilians have fled eastern neighbourhoods of the battered city since President Bashar al-Assad's regime began its controversial bombardment of the area in mid-November.

Overnight, government troops and allied forces seized the district of Tariq al-Bab where heavy fighting had raged a day earlier according to the Syrian Observatory for Human Rights.

The government has now recaptured around 60 percent of eastern parts of the city that the rebels overran in mid-2012, according to the Britain-based monitor.

With the rebels under fierce assault, the U.N. envoy for Syria suggested eastern Aleppo could fall to the government by the end of the year.

According to UN estimates, close to 30,000 people have been displaced by the latest fighting, 18,000 of them leaving to government-held areas and a further 8,500 going to the Kurdish-controlled neighborhood of Sheikh Maqsoud.

The escalating violence has been met with international outrage, including a UN warning that east Aleppo could become "a giant graveyard".

Moscow has announced several humanitarian pauses in Aleppo to allow civilians to flee, but until the recent escalation, only a handful did so.

Many civilians in the east previously expressed fear of leaving to government-held areas or through passages run by Moscow, which began a bombing campaign in support of Assad's forces in 2015.